To become proficient problem-solvers, physics students need to form a coherent and flexible understanding of problem situations with which they are confronted. Still, many students have only a limited representation of the problems on which they are working. Therefore, an instructional approach was devised to promote students' understanding of these problems and to support them in forming associations between problem features and solution methods. The approach was based on using the computer algebra software Mathematica as a tool for problem solving and visualization. An electrostatics course module was implemented based on this instructional approach, and this module was compared with a usual paper-and-pencil based one. Learning outcomes for both courses were not significantly different. The experimental course was found to impose a high cognitive load on the students. Based on the outcomes, proposals are made for ways in which the course could be improved.